Mathematica Wave eqaution PDE in mathematica

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The discussion revolves around the challenges of using Mathematica's DSolve to solve the wave equation with boundary conditions. The user reports that their input for the wave equation, including boundary conditions, returns unevaluated. A suggestion is made to first solve the partial differential equation (PDE) without the boundary conditions, which would yield a solution involving arbitrary functions C[1] and C[2]. These functions can then be determined using the specified boundary conditions. The conversation highlights the limitations of DSolve in handling PDEs directly with boundary conditions.
flasherffff
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hi
i can't make DSolve solve the wave equation with simple bvc
ive gone through the mathematica documentation and can't find the answer

for the input


\text{DSolve}\left[\left\{u^{(2,0)}[x,t]==4 u^{(0,2)}[x,t],u[x,0]==1,u^{(0,1)}[x,0]==\text{Sin}[x]\right\},u,\{x,t\}\right]
it just return it unevaluated
 
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DSolve's ability to deal with PDE's is a little limited. Try solving the PDE without the BCs. This will give a solution in terms of two functions, C[1] and C[2]. Then use the BCs to solve for those.
 

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